# An Improved Dingo Optimization Algorithm Applied to SHE-PWM Modulation Strategy

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Selective Harmonic Elimination Method

#### 2.2. Standard Dingo Optimization Algorithm (DOA)

#### 2.3. Modified Dingo Optimization Algorithm (mDOA)

Algorithm 1 Survival procedure |

1: Begin procedure 2: for $i=1$ to sizePopulation do3: if $survival\left(i\right)\le 0.3$ then4: if i is Even then5: Strategy 4: ${\overrightarrow{x}}_{i}$ search agent updated by Equation (9). 6: else7: Strategy 4: ${\overrightarrow{x}}_{i}$ search agent updated by Equation (10). 8: end if9: end if10: end for11: End procedure |

#### Pseudo Code for mDOA

Algorithm 2 Modified Dingo Optimizer Algorithm (mDOA) |

1: procedure DOA Taken from [27] and updated with our approach2: Initialization of parameters 3: $P=0.5$, probability of hunting or scavenger strategy 4: $Q=0.7$, probability of Strategy 1 (group attack) or Strategy 2 (persecution attack) 5: Generate the initial population 6: while iteration < Max Number of Iterations do7: if $random<P$ then8: if $random<Q$ then9: Strategy 1: Group Attack Procedure, Equation (5). 10: else11: Strategy 2: Persecution, Equation (6). 12: end if13: else14: Strategy 3: Scavenger, Equation (7). 15: end if16: Update search agents that have low survival value, Algorithm 1, Equation (9) or (10). 17: Calculate ${x}_{new}$, the fitness value of the new search agents 18: if ${x}_{new}<{x}_{*}$ then19: ${x}_{*}={x}_{new}$ 20: end if21: $iteration=iteration+1$ 22: end while23: Display ${x}_{*}$, the best optimal solution 24: end procedure |

## 3. Experimental Setup

## 4. Results

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**MLI staircase phase voltage output (black lines) and its relationship with an ideal pure sine waveform (red-dashed lines).

**Figure 4.**DOA and mDOA unimodal functions (${F}_{1}\phantom{\rule{4pt}{0ex}}\mathrm{to}\phantom{\rule{4pt}{0ex}}{F}_{4})$ convergence graph.

**Figure 10.**Sub-figure a to c show the experimental output waveform and harmonic spectrum of a three-phase eleven-level inverter at modulation index of 0.6, 0.8 and 1.

Algorithm | Angles | THD | Fitness | ||||
---|---|---|---|---|---|---|---|

${\alpha}_{\mathbf{1}}$ | ${\alpha}_{\mathbf{2}}$ | ${\alpha}_{\mathbf{3}}$ | ${\alpha}_{\mathbf{4}}$ | ${\alpha}_{\mathbf{5}}$ | |||

mDOA | 7.84 | 19.37 | 29.63 | 47.66 | 62.90 | 5.01 | 1.22 × 10${}^{-28}$ |

BWOA | 7.86 | 19.37 | 29.65 | 47.68 | 63.21 | 5.01 | 1.29 × 10${}^{-28}$ |

GWOA | 0.49 | 14.74 | 25.61 | 40.57 | 89.16 | 5.71 | 16.04 × 10${}^{-02}$ |

WOA | 4.19 | 20.29 | 22.12 | 41.97 | 61.15 | 6.90 | 3.93 × 10${}^{-02}$ |

Algorithm | Angles | THD | Fitness | ||||
---|---|---|---|---|---|---|---|

${\alpha}_{\mathbf{1}}$ | ${\alpha}_{\mathbf{2}}$ | ${\alpha}_{\mathbf{3}}$ | ${\alpha}_{\mathbf{4}}$ | ${\alpha}_{\mathbf{5}}$ | |||

mDOA | 9.71 | 33.42 | 43.28 | 61.16 | 83.59 | 5.62 | 3.01 × 10${}^{-29}$ |

BWOA | 9.70 | 33.43 | 43.30 | 61.18 | 83.60 | 5.63 | 3.05 × 10${}^{-29}$ |

GWOA | 10.32 | 31.83 | 44.74 | 62.23 | 85.65 | 6.73 | 3.37 × 10${}^{-03}$ |

WOA | 33.27 | 44.50 | 52.91 | 64.49 | 76.64 | 5.56 | 3.93 × 10${}^{-02}$ |

Algorithm | Angles | THD | Fitness | ||||
---|---|---|---|---|---|---|---|

${\alpha}_{\mathbf{1}}$ | ${\alpha}_{\mathbf{2}}$ | ${\alpha}_{\mathbf{3}}$ | ${\alpha}_{\mathbf{4}}$ | ${\alpha}_{\mathbf{5}}$ | |||

mDOA | 35.42 | 46.94 | 58.57 | 72.67 | 87.85 | 6.79 | 4.15 × 10${}^{-27}$ |

BWOA | 35.44 | 46.95 | 58.58 | 72.61 | 87.86 | 6.82 | 4.19 × 10${}^{-27}$ |

GWOA | 35.29 | 46.80 | 58.45 | 72.46 | 87.74 | 6.87 | 2.78 × 10${}^{-04}$ |

WOA | 35.35 | 46.89 | 58.49 | 72.44 | 87.70 | 6.87 | 8.17 × 10${}^{-05}$ |

**Table 4.**The p-values of the Wilcoxon rank-sum test with 5% significance for mDOA vs. BWOA, WOA, and GWOA. p-values ≤ 0.05 are shown in bold.

Modulation Index | BWOA | WOA | GWOA |
---|---|---|---|

0.5 | 0.023841866 | 0.334842127 | 0.994383367 |

0.525 | 0.202618429 | 0.688240195 | 0.363836258 |

0.55 | 0.013480336 | 0.402207261 | 0.805389527 |

0.575 | 0.893601743 | 0.568549239 | 0.805389527 |

0.6 | 0.838240614 | 0.320922266 | 0.418205544 |

0.625 | 0.915906103 | 0.228686857 | 0.08715687 |

0.65 | 0.677905357 | 0.035311051 | 0.007632168 |

0.675 | 0.70908377 | 0.010609836 | 0.00027332 |

0.7 | 0.046355344 | 2.63975 × 10${}^{-05}$ | 2.98839 × 10${}^{-05}$ |

0.725 | 0.116466135 | 2.12542 × 10${}^{-07}$ | 1.97051 × 10${}^{-07}$ |

0.75 | 0.587796526 | 0.006175451 | 0.002648716 |

0.775 | 0.442907971 | 0.008647429 | 0.002096522 |

0.8 | 0.251208826 | 0.006725085 | 0.000673813 |

0.825 | 0.617218971 | 0.084591112 | 0.010609836 |

0.85 | 0.783673018 | 0.103929294 | 0.010188301 |

0.875 | 0.174273548 | 0.007958048 | 0.001428464 |

0.9 | 0.927085867 | 0.039156639 | 0.049531746 |

0.925 | 0.418211405 | 0.00455584 | 0.27522748 |

0.95 | 0.161263208 | 0.000547578 | 0.126625679 |

0.975 | 0.257065744 | 0.133768379 | 0.169847032 |

1 | 0.023843633 | 0.022149345 | 0.000321759 |

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**MDPI and ACS Style**

Almazán-Covarrubias, J.H.; Peraza-Vázquez, H.; Peña-Delgado, A.F.; García-Vite, P.M.
An Improved Dingo Optimization Algorithm Applied to SHE-PWM Modulation Strategy. *Appl. Sci.* **2022**, *12*, 992.
https://doi.org/10.3390/app12030992

**AMA Style**

Almazán-Covarrubias JH, Peraza-Vázquez H, Peña-Delgado AF, García-Vite PM.
An Improved Dingo Optimization Algorithm Applied to SHE-PWM Modulation Strategy. *Applied Sciences*. 2022; 12(3):992.
https://doi.org/10.3390/app12030992

**Chicago/Turabian Style**

Almazán-Covarrubias, Juan H., Hernán Peraza-Vázquez, Adrián F. Peña-Delgado, and Pedro Martín García-Vite.
2022. "An Improved Dingo Optimization Algorithm Applied to SHE-PWM Modulation Strategy" *Applied Sciences* 12, no. 3: 992.
https://doi.org/10.3390/app12030992